It is remarkable that a model with spontaneous symmetry
breaking at a relatively low (i.e. TeV) scale can pass the experimental
bounds upon
it coming from flavour constraints. Such constraints are notoriously strict
when they involve flavour transitions of the first two generations of
electrically charged fermionic fields, particularly from \(K-\overline{K}\) 
mixing [1]}.
Moreover, the strength of LHC bounds coming from bump hunts in the di-muon
mass spectrum resulting from \(pp \rightarrow Z^\prime \rightarrow \mu ^+ \mu ^-\) 
is diminished by the fact that the \(Z^\prime \)  only
couples with an appreciable strength to third family fermions. Thus,
the
dominant LHC production process (as depicted in the middle panel of figure REF ) originates from
fusing a bottom quark \(b\)  and
an anti-bottom quark \(\bar{b}\)  in the initial proton states, providing double
suppression to the \(Z^\prime \)  production cross section from small
(anti-)bottom parton distribution
functions [2]}. Current direct searches imply a lower bound upon
the \(Z^\prime \)  mass \(M_{Z^\prime }\) 
of around 1-2 TeV [3]}, [4]}, [5]}, [6]}, significantly lower than \(Z^\prime \)  models in which
the \(Z^\prime \)  field couples to quarks universally, where the current lower
bound from ATLAS and CMS is currently
around 5 TeV [7]}, [8]}. A window in the parameter space
with 20 GeV \(<M_{Z^\prime }<\)  300 GeV [3]}, [4]}
is all but ruled out at the
\(95\%\)  confidence level [5]}. A recent
analysis [6]} found that
although through much of the parameter space the \(Z^\prime \)  can be
discovered at the HL-LHC, either a 3 TeV \(\mu ^+\mu ^-\) 
collider, a
10 TeV
\(\mu ^+\mu ^-\) 
collider [13]} or a 100 TeV FCC-hh
collider
[14]} would cover all of the parameter space compatible with
the model's
explanation of the \(b\rightarrow s \mu ^+\mu ^-\) 
anomalies.
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